What is the answer to x2^{3x-1}=4^x ?

The answer to x2^{3x-1}=4^x is x=1

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x2^{3x-1}=4^x

x 2^{3 x - 1} = 4^{x}

x = 1

Solution steps

x \cdot 2^{3 x - 1} = 4^{x}

Apply exponent rules

x \cdot 2^{3 x - 1} = (2^{2})^{x}

Subtract

2^{2 x}

from both sides

x \cdot 2^{3 x - 1} - 2^{2 x} = 2^{2 x} - 2^{2 x}

Simplify

x \cdot 2^{3 x - 1} - 2^{2 x} = 0

Factor

x \cdot 2^{3 x - 1} - 2^{2 x} : 4^{x} (2^{x - 1} x - 1)

4^{x} (2^{x - 1} x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

4^{x} = 0 or 2^{x - 1} x - 1 = 0

Solve

4^{x} = 0 :

No Solution for

x \in R

Solve

2^{x - 1} x - 1 = 0 : x = 1

x = 1

4^{3 x + 1} = 6^{1 - 2 x}

5^{x - 9} = 3

1.0 9^{x} = 1.5

4^{- 3 v - 2} = 4^{- v}

e^{12 x} = 2